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BOUNDED POLYNOMIALS AND HOLOMORPHIC MAPPINGS BETWEEN CONVEX SUBRINGS OF *$\mathbb{C}$

Published online by Cambridge University Press:  08 February 2018

ADEL KHALFALLAH  and
SIEGMUND KOSAREW
ADEL KHALFALLAH
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS DHAHRAN31261, SAUDI ARABIAE-mail:khelifa@kfupm.edu.sa
SIEGMUND KOSAREW
Affiliation:
INSTITUT FOURIER, UNIVERSITÉ GRENOBLE ALPES 100 RUE DES MATHS 38610 GIÈRES, FRANCEE-mail:siegmund.kosarew@ujf-grenoble.fr
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Abstract

Using convex subrings of *$\mathbb{C}$, a nonstandard extension of $\mathbb{C}$, we define several kinds of complex bounded polynomials and we provide their associated analytic functions obtained by taking the quasistandard part.

Keywords

46F3026E3503H0546S1012J25nonstandard analysisinternal polynomialsgeneralized holomorphicity
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 372 - 384
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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